Related papers: Beyond $\underTilde{\Sigma}^2_1$ absoluteness
This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework…
Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely,…
We define the property of Pi_2-compactness of a statement phi of set theory, meaning roughly that the hard core of the impact of phi on combinatorics of aleph_1 can be isolated in a canonical model for the statement phi. We show that the…
A usual dichotomy is that in many cases, reasonably definable sets, satisfy the CH, i.e. if they are uncountable they have cardinality continuum. A strong dichotomy is when: if the cardinality is infinite it is continuum as in [Sh:273]. We…
We investigate sentences which are simultaneously partially conservative over several theories. First, we generalize Bennet's results on this topic to the case of more than two theories. In particular, for any finite family $\{T_i\}_{i \leq…
Foreman proved the Duality Theorem, which gives an algebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of $\omega_1$ is preserved by any proper forcing. We…
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…
It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…
Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.
The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…